) Expected value A casino is running a new game that has the following prizes and probabilities. The table show wins and losses for the casino players at the game and the respective probabilities. Table 1: Probability Distribution of Prizes X. P(X=x) - £23 0.3 - £10. 0.4 £25. 0.2 £42. 0.1 (a) Calculate the expected value of this game. (b) Imagine that you played this game and got: -£23, -£23, £42. This means that you won on average £14.6. Why is this different from the expected value calculated in a)? Relate the concept of sample average to that of the expected value. (c) Would it be profitable for the Casino owner in the long run to offer this game? Why?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
1) Expected value
A casino is running a new game that has the following prizes and
probabilities. The table show wins and losses for the casino
players at the game and the respective probabilities.
Table 1: Probability Distribution of Prizes
X. P(X=x)
- £23 0.3
- £10. 0.4
£25. 0.2
£42. 0.1
(a) Calculate the expected value of this game.
(b) Imagine that you played this game and got: -£23, -£23, £42.
This means that you won on average £14.6. Why is this
different from the expected value calculated in a)? Relate
the concept of sample average to that of the expected value.
(c) Would it be profitable for the Casino owner in the long run to
offer this game? Why?
(d) Calculate the variance of this game.
(e) A new manager decides to increase all outcomes (both
positive and negative) by 30%. Calculate the new expected
value and variance of the above game. Is this a wise move
for the Casino in the long run? Why?
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